There are times when we forgive and forget - I do not mean forget that someone offended you but you forget to love them after you have forgiven them.
Biblical forgiveness is never just "not holding that sin against the person" and then not having anything to do with them any more or holding a grudge against them - just to show them that while you have forgiven them, you have not forgotten and you will bring a little retribution of your own.
We look at two passages - the first one describes God's forgiveness and the second of the forgiveness that is demanded of by the believer.
Psalm 103.1-5: Praise the LORD, O my soul; all my inmost being, praise his holy name. 2 Praise the LORD, O my soul, and forget not all his benefits- 3 who forgives all your sins and heals all your diseases, 4 who redeems your life from the pit and crowns you with love and compassion, 5 who satisfies your desires with good things so that your youth is renewed like the eagle's.
Colossians 3.12-14: Therefore, as God's chosen people, holy and dearly loved, clothe yourselves with compassion, kindness, humility, gentleness and patience. 13Bear with each other and forgive whatever grievances you may have against one another. Forgive as the Lord forgave you. 14And over all these virtues put on love, which binds them all together in perfect unity.
Psalm 103 describes God's forgiveness as not only "not holding our sins against us" but granting us benefits: healing diseases, redeeming, crowning you with love and compassion and satisfying your life with good things. Colossians 3 tells us that God's people are to be compassionate, kind, humble, gentle and patient, putting on love - even to those who they must forgive.
What does Scripture teach us? Forgive and DO NOT FORGET - that is do not forget to satisfy the one who has offended you with good things, being kind and gentle and patient - above all loving them. This may take time but that is how radical Christian forgiveness is as we experience it from Jesus and read of it in His Word.